Molecules, Molecules

Organic molecules can be amazingly complex, and picturing them takes a great variety of shapes and conventions, especially when we want to show details of their 3-dimensional structure. If we stay with reasonably simple compounds, meaning those with only single bonds between atoms, we can draw them on a rectangular grid with every bond running horizontally or vertically. In such a molecule carbon is bonded to four adjacent atoms, nitrogen to 3, oxygen to 2 and hydrogen to 1.

A bond joins two atoms that sit in horizontally or vertically neighbouring cells, and the same pair of atoms is bonded at most once. Neighbouring atoms are not forced to bond. A grid represents a valid molecule when the bonds can be chosen so that every atom reaches exactly its own number of bonds.

Not every grid represents a valid molecule. Write a program that decides whether a given grid does.

The input holds a series of possible molecules drawn as grids. The first line for each molecule holds two integers r and c ($1 \le r, c \le 5$), the number of rows and columns of the rectangle that follows. The next r lines contain c characters each, taken from . (empty), H (hydrogen), O (oxygen), N (nitrogen) and C (carbon). The input ends with a line containing two zeroes.

A grid classified as valid need not be physically realisable, and one grid may hold more than one molecule.

For each potential molecule, print one of the following lines:

Molecule <num> is valid.
Molecule <num> is invalid.

where <num> is a running number starting at 1.